This invention relates to solid-state (IC) band-gap voltage references for providing an output voltage which is substantially constant with changes in temperature. More particularly, this invention relates to band-gap references provided with temperature compensation means to minimize changes in output voltage with changes in temperature.
Solid-state IC references have been developed which rely on certain temperature-dependent characteristics of the base-to-emitter voltage (V.sub.BE) of a transistor. For example, in U.S. Pat. No. 3,617,859, an IC reference is described in which a diode-connected transistor and a second transistor are operated at different current densities to develop a voltage across a resistor proportional to the difference in the respective base-to-emitter voltages (.DELTA.V.sub.BE). This difference voltage has a positive temperature coefficient (TC), and is connected in series with the V.sub.BE voltage of a third transistor. The latter voltage has a negative TC which counteracts the positive TC of the first voltage to produce a composite voltage with a relatively low TC and serving as the output of the reference.
In U.S. Pat. No. 3,887,863, issued to the present applicant, a three-terminal band-gap reference is disclosed using a band-gap cell requiring only two transistors. These transistors are connected in a common base configuration, and the ratio of current densities in the two transistors is automatically maintained at a desired value by an operational amplifier which senses the collector currents of the two transistors. A voltage responsive to the .DELTA.V.sub.BE of the two transistors is developed across a resistor, and that voltage is connected in series with the V.sub.BE voltage of one of the two transistors, resulting in a combined output voltage with a very low temperature coefficient.
The mathematical relationships regarding the variation of voltage with temperature in band-gap devices commonly are simplified for purposes of analysis by ignoring certain terms of the basic equation, as expressing only secondary non-significant effects. For example, in the above U.S. Pat. No. 3,617,859, column 4, line 6, it is explained that the last two terms of the given expression are deleted because they are considered to be insignificant. However, although the effects of such secondary terms are small, they are real, and can be important in some applications. Thus, it is desired to provide a way to avoid variations in output voltage corresponding to such secondary and presently uncompensated effects.
The mathematical analysis of the problem when retaining the commonly-ignored terms is somewhat involved, as can be seen in the article by the present applicant published in the IEE Journal of Solid-State Circuits, Vol. SC-9, No. 6, December 1974, and entitled "A Simple Three-Terminal IC Band-gap Reference". Proper expressions can, nevertheless, be developed for the output voltage, and the first and second derivatives thereof with respect to temperature, as shown in the following Equations 12-14 from that article: EQU E=V.sub.go +(T/T.sub.o)(V.sub.BEo -V.sub.go)+(m-1)(kT/q)ln(T.sub.o /T)+(P.sub.1 +1)(R.sub.1 /R.sub.2)(kT/q)LN(J.sub.1 /J.sub.2) (12) EQU dE/dT=(1/T.sub.o)(V.sub.BEo -V.sub.go)+(P.sub.1 +1)(R.sub.1 /R.sub.2)(k/q)ln(J.sub.1 /J.sub.2)+(m-1)(k/q)ln(T.sub.o /T)-1 (13) EQU d.sup.2 E/dT.sup.2 =-(m-1)(k/q)(1/T). (14)
With values of m greater than one (a realistic assumption), equation (14) implies a non-zero temperature coefficient at temperatures other than T.sub.o. However, it will be evident from the above considerations that the output voltage varies with temperature in such a way that an exact compensation for such variation would require quite complex circuitry, too costly for most applications.
Accordingly, it is an object of the present invention to provide a band-gap reference with improved compensation for its inherent temperature characteristic.